POLARIZATION Only transver transverse se waves may become polarized.
ELECTROMAGNETIC WAVE: WAVE: LIGHT LIGHT EM waves are periodic changes of electric and magnetic fields in space and time.
EM waves is transverse waves.
ELECTROMAGNETIC WAVE: WAVE: LIGHT LIGHT EM waves are periodic changes of electric and magnetic fields in space and time.
EM waves is transverse waves.
Techniques to obtained Polarised Light
1.Polarisation by Reflection 2.Polarisation by Refraction 3.Polarisation by Double Refraction 4.Polarisation by Scattering
Brewster’s Law The tangent of the angle of polarization is numerically equal to the refractive index of the medium.
tan i p i
i
X
Y
By Snell’s Law
sin i p sin r
Comparing these two equations
sin i p cosi p
sin i p sin r
sin r cos i p o
sin r sin(90 r i p
i p ) o
90
o
XOY 90
The maximum polarization (vibration in one plane only) of a ray of light may be achieved by letting the ray fall on a surface of a transparent medium in such a way that the refracted ray makes an angle of 90° with the reflected ray
Malus Law When a completely plane –polarized light is incident on an analyzer, the intensity of the emergent light varies as the square of the cosine of the angle between the planes of transmission of the analyzer and the polarizer.
The angle between the transmission axis of the analyzer and the polarizer is θ. Eo is the amplitude of the electric vector transmitted by the polarizer. Intensity, Io of the light incident on the analyzer is I o
2
E o
The electric field vector E0 can be resolved into two rectangular components i.e E0 cosθ and E0 sinθ. The analyzer will transmit only the component ( i.e E0 cosθ ) which is parallel to its transmission axis. However, the component E0sinθ will be absorbed by the analyser.
Therefore, the intensity of light transmitted by the analyzer .
I ( E o cos )
2
I I o cos 2 When θ = 0° ( or 180° ), I = I0 cos2θ = I0 That is the intensity of light transmitted by the analyzer is maximum when the transmission axes of the analyzer and the polarizer are parallel. When θ = 90°, I = I0 cos290° = 0 That is the intensity of light transmitted by the analyzer is minimum when the transmission axes of the analyzer and polarizer are perpendicular to each other.
DOUBLE REFRACTION The splitting of unpolarised light into two refracted component (ordinary light and extraordinary light) travelling at different speeds inside medium is known as phenomenon of double refraction. This is observed using a special crystal category known as doubly refracting crystal. POSITIVE CRYSTAL (re < ro) AND NEGATIVE CRYSTAL (re > ro)
Properties of O ray and E-rays
Two different angle of refraction , i.e. re and ro
Both rays becomes parallel after emerging the crystal
Ordinary follows the ordinary law of refraction but not the extraordinary.
Both rays are plane polarised. Ordinary ray : Plane of vibration is perpendicular to the principal section while for extraordinary is parallel to the principal section.
POSITIVE CRYSTAL (re < ro ; μe > NEGATIVE CRYSTAL (re > ro;
μ0)
AND
DOUBLE REFRACTIVE CRYSTALS
Colorless Calcite Rhombohedron with a long edge of ~12 cm.
The double refractive property of calcite leads to the formation of two images as shown in these examples. The images are related to the existence of ordinary rays ( orays) and extraordinary rays (e-rays). An analysis of these rays shows that both these rays are linearly polarized.
Optic Axis – A line passing throgh any one of the blunt corners and making equal angles with each of three edges which meet at the corner is known as optic axis
Principal Section –
A plane containing the optic axis of the crystal and perpendicular to the two opposite refracting faces is called principal section of the crystal for that pair of faces:
Birefringent devices – Separation of the o - and e - rays.
NICOL PRISM-Construction
Thin layer of balsam cement with μ = 1.55
For calcite, again,
μ e
= 1.486,
μ o
= 1.658
A calcite crystal that is cut, polished, and painted, separates the o-ray and eray via TIR (total internal reflection). A thin layer of balsam glues two halves of the crystal. Balsam has an index of refraction, μ b, which is between that of the o- and e-rays, i.e., μ e < μ b < μ o. Thus, the o-ray experiences TIR at the balsam interface and is absorbed by the layer of black paint on the side. The e-ray refracts normally at the balsam interface an leaves the crystal at the bottom. Therefore, the emitted ray can be used as a fully linearly polarized beam.
NICOL PRISM - Working o-ray absorping paint
e-ray
Air gap
This prism is similar to the Nicol, prism but without the use of balsam cement.
Polarizers take advantage of double refraction and total internal reflection Combine two prisms of calcite, rotated so that the ordinary polarization in the first prism is extraordinary in the second (and vice versa). The perpendicular polarization goes from high index (n ) to low (n ) and undergoes total internal reflection, while the parallel polarization is transmitted near Brewster's angle. o
e
Nicol Prism: made up from two prisms of calcite cemented with Canada balsam. The ordinary ray totally reflects off the prism boundary, leaving only the extraordinary ray.
Production of Polarised light x=a cos (ωt) y=b cos (ωt-δ)
x
2
a
2
y
2
b
2
2 xy ab
2
cos sin
General eqution of Ellipse
PLANE POLARISED LIGHT IN A VERTICAL PLANE
The intersecting plane looked at from the front.
PLANE POLARISED LIGHT IN A HORIZONTAL PLANE
The intersecting plane looked at from the front.
Superposition
of
plane-polarized
waves.
When two electromagnetic waves plane-polarized in two perpendicular planes are present simultaneously then the electric fields are added according to the rules of vector addition, 'parallelogram rule' (superposition) .
The intersecting plane looked at from the front.
CIRCULARLY POLARISED LIGHT: CLOCKWISE Superposition of plane-polarized waves . The superposition of two waves that have the same amplitude and wavelength and are polarized in two perpendicular planes but there is a phase difference of 3π/2, 7π/2…… degrees between them. A phase difference of 3π/2 or -90° means that when one wave is at its peak then the other one is just crossing the zero line. Right polarization.
The intersecting plane
CIRCULARLY POLARISED LIGHT: ANTICLOCKWISE Superposition of plane-polarized waves 3. The following animation shows what happens when the two waves shown on the previous page are added with a phase difference of π/2, 5π/2 degrees
The intersecting plane looked at from the front.
Circular polarization
Circularly polarized waves The animations presenting the two types of circularly polarized light are shown together so that you can compare them more easily.
•
Superposition of circularly polarized waves when a left circularly polarized wave and a right circularly polarized wave are added.
• As we see, the result of superposing two circularly polarized waves is a plane polarized wave.
The intersecting plane
Retardation Plates 1.Quarter Wave Plate A plate of a doubly refracting crystal where refracting faces are cut parallel to the direction of optic axis whose thickness is such that to produce a phase difference of π /2 and a path difference of λ /4 between the ordinary and extraordinry waves is called quarter wave plate.
t=λ /4(μE ~ μo) 1.Half Wave Plate t=λ /2(μ ~ μ )
Analysis of Polarised light General Light
Rotating Nicol
No Intensity variation
Either circularly or unpolarised
Intensity variation with min zero intensity
Intensity variation with min non-zero intensity
Plane Polarised
Either elliptically or partially plane polarised
Either circularly or unpolarised
Either Elliptically or partially polarised light
Incident on quarter wave plate and then through rotating nicol
Incident on quarter wave plate and then through rotating nicol
Intensity variation with min zero intensity
No intensity variation
Intensity variation with min zero intensity
Intensity variation with minimum nonzero
Circularly Polarised
Unpolarised
Elliptically Polarised
Partially polarised
LECTURES TO BE PREPARED BY THE STUDENTS
L-13 & L-14 Optical Activity Specific rotation Polarimeters
Consider hypothetical point sources of natural light embedded within negative and positive uniaxial crystals, as shown in the left and right figures.
The shape of the ellipsoids depends on sign of
n
(+ or -) as shown.
